标题： 过确定性椭圆问题在模型黎曼流形上的研究 显示英文标题

标题： Overdetermined elliptic problems on model Riemannian manifolds

摘要： 我们在模型黎曼流形的超定椭圆问题背景下建立了一个关于环扇形区域的刚性定理。 具体来说，如果这样一个区域允许一个非齐次Helmholtz方程的解同时满足恒定Dirichlet和恒定Neumann边界条件，则该区域必然是球面扇形，并且解必然是径向对称的。 这一结果强调了超定边界条件所施加的强大几何约束，将经典的刚性现象扩展到了这个更一般的框架中。 显示英文摘要

摘要： We establish a rigidity theorem for annular sector-like domains in the setting of overdetermined elliptic problems on model Riemannian manifolds. Specifically, if such a domain admits a solution to the inhomogeneous Helmholtz equation satisfying both constant Dirichlet and constant Neumann boundary conditions, then the domain must be a spherical sector, and the solution must be radially symmetric. This result underscores the strong geometric constraints imposed by overdetermined boundary conditions, extending classical rigidity phenomena to this more general framework.